7. ELLIPTICITY

The inferred LMC viewing angles can be used to deproject the observed
morphology that is seen in projection on the sky
(van der Marel 2001).
This yields an in-plane ellipticity
in the range
~ 0.2-0.3, depending somewhat on the adopted viewing angles; e.g., the
Nikolaev et al. (2004)
angles give
= 0.21 and the
van der Marel & Cioni
(2001)
angles give
= 0.31. The
conclusion that the LMC is elongated is in itself not surprising. The
dark matter halos predicted by cosmological simulations are generally
triaxial (e.g.,
Dubinski & Carlberg
1991),
and the gravitational
potential in the equatorial plane of such halos does not have circular
symmetry. So it is generally expected that disk galaxies are elongated
rather than circular. Furthermore, it is possible to construct
self-consistent dynamical models for elliptical disks (e.g.,
Teuben 1987).
What is surprising is that the LMC ellipticity is fairly
large. Studies of the apparent axis ratio distribution of spiral
galaxy disks
(Binney & de
Vaucouleurs 1981;
Lambas, Maddox &
Loveday 1992)
of the structure of individual spiral galaxies
(Rix & Zaritsky 1995;
Schoenmakers, Franx &
de Zeeuw 1997;
Kornreich, Haynes &
Lovelace 1998;
Andersen et al. 2001)
and of the scatter in the Tully-Fisher relation
(Franx & de Zeeuw 1992)
indicate that the
average (deprojected) ellipticity of spiral galaxies is only
5-10%. So while spiral galaxies are generally elongated, their
elongation is usually smaller than inferred here for the LMC. Of
course, galaxies of type Sm and Im are (by definition) more irregular
and lopsided than spirals. So it is not a priori clear whether or not
the LMC is atypically elongated for its Hubble type.

It is interesting to ask what may be the cause of the large in-plane
ellipticity of the LMC. The prime candidate is distortion by the Milky
Way tidal field. The present-day tidal force on the LMC by the Milky
Way exceeds that from the SMC. Moreover, the Milky Way tidal field is
responsible for other well-known features of the Magellanic system,
such as the Magellanic Stream (see Section 3).
N-body simulations have shown that the structure of the LMC can be altered
significantly by the Milky Way tidal force
(Weinberg 2000)
and the simulations of
Mastropietro et al. (2004)
indeed predict a
considerable in-plane elongation for the LMC. Also, the LMC elongation
in projection on the sky points approximately towards the Galacic
Center and is perpendicular to the Magellanic Stream
(van der Marel 2001),
as predicted naturally by simulations of tidal effects
(Mastropietro et al. 2004).
However, a very detailed data-model
comparison is not possible at the present time. That would require
accurate knowledge of the past history as a function of time of the
LMC orbit, of the disk-plane orientation due to
precession and nutation, and of the LMC-SMC distance. Such knowledge is not available
at the present time.

A consequence of the ellipticity of the LMC disk is that one cannot
expect the streamlines of tracers in the disk to be perfectly
circular, by contrast to what has been assumed in all kinematical
studies to date. The effect of this is probably not large, because the
gravitational potential of a mass distribution is always rounder than
the mass distribution itself. One effect of ellipticity is an apparent
offset between the kinematical line of nodes and the true line of nodes
(Schoenmakers, Franx &
de Zeeuw 1997).
This effect is presently not at observable levels, given that
kinematical analysis of carbon stars (see
Section 5) yields a line-of-nodes position
angle that is in
adequate agreement with geometrical determinations (see
Section 6). However, it should be kept
in mind that, as the sophistication of the studies of LMC kinematics increases, it might become necessary
to account for the effect of non-circularity on the observed kinematics.